13/12

Interval information

Ratio	13/12
Factorization	2-2 × 3-1 × 13
Monzo	[-2 -1 0 0 0 1⟩
Size in cents	138.5727¢
Name	tridecimal neutral second
Color name	3o2, tho 2nd
FJS name	[math]\displaystyle{ \text{m2}^{13} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	7.2854
Weil height (log2 max(n, d))	7.40088
Wilson height (sopfr(nd))	20
[sound info]
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In 13-limit just intonation, 13/12 is the tridecimal neutral second of about 138.6¢. It is a superparticular interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between 13/8 and 3/2 in the octave). It is flat of the 11-limit lesser neutral second of 12/11 by 144/143 (about 12.1¢), and sharp of the 13-limit large semitone of 14/13 by 169/168 (about 10.3¢).

The neutral second in 17edo is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.

See also

• 24/13 – its octave complement
• 18/13 – its fifth complement
• Gallery of just intervals
• List of superparticular intervals